rmulaUrl":null,"initialIndex":40,"initialQuestionWindow":[{"id":"953ef71f-90e5-4ad0-9ee1-abba2d6f45ec","revisionId":"79ea1c7d-6aff-467a-b7a0-1c4931a8b443","questionNumber":null,"questionType":"LA","specification":"A force of $5.4\\text{ N}$ is applied to stretch a metal spring.\nThe extension of the spring is $0.09\\text{ m}$.","difficulty":3,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"05bfaca4-9b88-43fb-982a-c4e47fefc196","label":null,"content":"Calculate the spring constant, $k$, of the spring and state the unit.\n\nUse the equation:\n$$F = k \\times e$$","markscheme":"- Rearranges the equation or substitutes values to give $k = \\frac{5.4}{0.09}$ M1\n- Calculates the value $k = 60$ A1\n- States the unit of the spring constant as $\\text{N/m}$ (or $\\text{N m}^{-1}$) B1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"rearrange_hookes_law","label":"Rearrange Hooke's law","steps":[{"type":"text","order":1,"title":"Choose the unknown","content":"The equation is $F = k \\times e$. Here, $k$ is the spring constant, $F$ is the force, and $e$ is the extension.\n\nWe need to make $k$ the subject. Dividing by $e$ undoes the multiplication by $e$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=given-equation}{F=k\\times e}"},{"latex":"\\htmlData{anchor=rearranged-equation}{k=\\frac{F}{e}}"},{"latex":"\\htmlData{anchor=substitution}{k=\\frac{5.4}{0.09}}"}],"highlights":[{"color":"green","style":"box","anchor":"substitution"}],"connections":[{"to":"rearranged-equation","from":"given-equation","color":"orange","label":"divide by e"}]},"order":2,"title":"Rearrange and substitute","description":"Divide both sides by the extension, then put in the given force and extension. This substitution earns the first mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"k = \\frac{5.4}{0.09}"},{"latex":"\\htmlData{anchor=answer}{k = 60\\ \\mathrm{N/m}}"}],"highlights":[{"color":"green","style":"box","anchor":"answer"}]},"order":3,"title":"Calculate the constant","description":"Now divide the force by the extension. The value earns A1 and the unit earns B1."}]}],"generatedAt":"2026-07-22T12:12:28.818Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"993e0f14-807b-40d8-91ed-f05ef4f2c1ff","revisionId":"b5d15687-ee66-4fd1-ac46-813a9e1be800","questionNumber":null,"questionType":"LA","specification":"An engineer is calibrating a heavy-duty seismic dampening spring in a structural testing rig.","difficulty":3,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"4f4f1ada-0847-4712-8b8e-f743ba5815a1","label":null,"content":"State the two physical measurements that must be made to determine the extension of this spring when a \$2.5\\text{ kN}\$ calibration load is suspended from it.","markscheme":"- The original (unstretched) length of the dampening spring before the load is applied. B1\n- The extended (stretched) length of the spring while the $2.5\\text{ kN}$ calibration load is suspended. B1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"measure_lengths","label":"Measure the two lengths","steps":[{"type":"drawing","order":0,"title":"Compare the two lengths","width":824,"height":452,"shapes":[{"id":"seg-S1LS1R","type":"line","color":"black","points":[{"x":211,"y":91.2},{"x":397.7,"y":91.2}]},{"id":"seg-T1B1","type":"line","color":"blue","points":[{"x":304.3,"y":91.2},{"x":281,"y":123.8}]},{"id":"seg-B1C1","type":"line","color":"blue","points":[{"x":281,"y":123.8},{"x":327.7,"y":156.5}]},{"id":"seg-C1D1","type":"line","color":"blue","points":[{"x":327.7,"y":156.5},{"x":281,"y":189.2}]},{"id":"seg-D1E1","type":"line","color":"blue","points":[{"x":281,"y":189.2},{"x":304.3,"y":221.8}]},{"id":"seg-M1TM1B","toX":243.7,"toY":221.8,"type":"arrow","color":"blue","fromX":243.7,"fromY":91.2},{"id":"seg-M1TM1B-re

Forces and springs

Question 21

Forces and springs Questions

Forces and springs

Question 21

Forces and springs Questions